THE EFFECT OF REFERENCE FRAME SELECTION ON … · THE EFFECT OF REFERENCE FRAME SELECTION ON MODELLED TURBULENCE FOR GROUND EFFECT AERODYNAMICS SIMULATIONS ... process and only the

THE EFFECT OF REFERENCE FRAME SELECTION ON MODELLEDTURBULENCE FOR GROUND EFFECT AERODYNAMICS

SIMULATIONS

Tracie BarberSchool of Mechanical Engineering

University of New South WalesNSW 2052 Australia

[email protected]

James KeoghSchool of Mechanical Engineering

University of New South WalesNSW 2052 Australia

[email protected]

John ReizesSchool of Mechanical Engineering

University of New South WalesNSW 2052 Australia

[email protected]

ABSTRACTThe principle of aerodynamic reciprocity is founda-

tional in the study of fluid mechanics. A wind tunnel frame-work is generally used to test aerodynamic performance andthis body-stationary convention has continued into the com-putational regime. However, there is no practical reasonwhy the moving body/stationary fluid situation that corre-sponds to reality cannot be used for computational mod-elling. When the concept of ground effect aerodynamics isstudied, an extra boundary is required which must move,and the extra boundary condition also adds complexity toa computational simulation. The introduction of freestreamturbulence, as well as possible additional turbulent genera-tion from the moving ground, raise the possibility of spu-rious turbulent values, particularly when calculated using aRANS based closure in a CFD model. Here, a ground ef-fect aerodynamics study is undertaken computationally, us-ing a body-stationary and a body-moving reference frame,to examine any variation that occurs. Two models for tur-bulence are implemented, the Realizable k-ε model and theReynolds Stress Model (RSM).

INTRODUCTIONGround effect aerodynamics, in which a lifting surface

operates in close proximity to the ground, has relevanceto aircraft landing and takeoff, automotive operations (es-pecially high-speed racing conditions) and also to the de-sign and operation of wing in ground vehicles, or ekra-noplans. Simulations of ground effect aerodynamics aresomewhat complicated by the need for a moving ground,if a body-fixed reference frame is used - standard for mostaerodynamic investigations. Experimentally, this involvesthe construction and careful implementation of a conveyorsystem on the lower floor of the wind tunnel (Diasinos et al.,2005), while computationally the implementation of a mov-ing ground is relatively straightforward. For a computa-tional solution, the accurate and appropriate specification

of boundary conditions is an important part of the solutionprocess and only the ground moving condition accuratelysimulates ground effect aerodynamics (Barber et al., 1999)(however studies still occur where stationary ground modelsare used (Pillai et al., 2014)).

In general, for lifting wings near the ground, increasedlift and increased lift to drag ratio when approaching theground are found (Ahmed et al., 2007). Early work inthe field of ground effect frequently made use of incorrectboundary conditions on the ground, leading to consider-able confusion around the mechanisms causing the changein aerodynamics performance (Barber et al., 2002). Pre-vious work exclusively utilises body-stationary approachesfor both experimental and computational analyses.

The use of a body-stationary reference frame is themost commonly used system of aerodynamic simulation(though not necessarily in naval architecture where towingtanks are common), using either a body-fixed wind tunnelor body-fixed CFD situation to simulate the real-life case ofa body moving through a fluid. This principle of aerody-namic reciprocity was defined in the 16th century, when DaVinci proposed that fluid flow is the same whether the bodymoves through a medium at a given velocity or the mediumflows past the stationary body at the same velocity (Gia-comelli, 1930). While the methodology is well-accepted,the widespread commonality of the body-fixed solution andthe subsequent explanation of the flow features based onthe flow characteristics seen in this reference frame couldbe problematic in certain cases. In particular, when the sit-uation being examined includes another boundary, whichalso must be taken into a different reference frame (suchas in ground effect aerodynamics), the body-fixed explana-tions may obscure the true nature of the flow regime (Close& Barber, 2014). The explanation of such characteristicscause confusion to those unfamiliar with the change in ref-erence frame, and in some cases the cause and effect of theflow properties may be improperly or poorly explained.

A further consideration relates to the possible introduc-

1

June 30 - July 3, 2015 Melbourne, Australia

9P-07

tion of greater levels of turbulence into the flow field, due toa moving surface on the ground boundary. Reducing levelsof free-stream turbulence (or often simply unsteadiness), isa well-known component to wind tunnel design. In a mov-ing ground wind tunnel, the free-stream air and additionally,the lower surface of the wind tunnel are moving, and poten-tially turbulent generators. The use of RANS turbulenceclosures may also contribute further numerical error in theirtreatment of the generation terms for these moving surfaces.

While more sophisticated models for turbulence suchas DES and LES are increasingly seeing use in the study ofground effect aerodynamics, RANS models are still com-monplace, and particularly the use of eddy-viscosity basedmodels (Qu et al., 2015; Doig et al., 2014; Lee & Lee, 2013;Qu et al., 2014).

The purpose of this study is to re-examine ground ef-fect in both a body-stationary reference frame and a body-moving reference frame to determine if any discrepanciesmay occur.

METHODOLOGYTwo three-dimensional models are developed: the first

is called “stationary”, indicating that the airfoil is station-ary with the fluid moving past it, and the second is called“moving”, indicating that the airfoil is moving in a still at-mosphere. It is possible to simulate a stationary flow fieldby using a moving reference frame model. Although in-tended for use in turbomachinery studies for rotor-stator in-teraction, the constant velocity of an airfoil moving throughstationary air is simulated by implementing a steady veloc-ity of the coordinate system attached to the wing. The mainvariation is that rather than using the absolute velocity, therelative velocity is employed in the conservation equationsand it is given by

Vr = V −Vt (1)

in which Vt is the translational velocity of the frame ofreference attached to the airfoil, so the equations of conti-nuity and momentum are then written in the relative frame.

The test-case used is a computational model basedon detailed experimental data obtained by Zerihan (Zeri-han & Zhang, 2000). A chord length of 223.4 mm andspan of 1100 mm gave an aspect ratio of 4.92, and theinverted T026 wing is studied at 3.45o angle of incidenceand a clearance of h/c (height/chord) = 0.179. Computa-tional models are run as symmetric about the wing midspanand the freestream air conditions matched those used in theSouthampton Low-Speed Wind Tunnel (Zerihan & Zhang,2000). The pressure-based implicit coupled solver wasutilised to achieve steady-state simulations. Simulationswere run using a second-order node-based upwinding dis-cretization scheme and the convergence criteria set for whenaerodynamic forces ceased to change by more than 0.02%over 1000 continued iterations, and a point velocity mon-itor placed near the centre of the prominent lower vortexalso ceased to change by more than 0.02%. The simulationswere solved across 64 processors on the UNSW AustraliaTrentino cluster.

The calculated Reynolds number for the simulations(based on chord-length) was of 4.54x105. In the experi-mental setup a grit strip was located at 0.1c on both the

pressure and suction surfaces of the wing was used to en-able transition and this was computationally modelled forthe validation (further models used a fully turbulent do-main). The reader is directed to our earlier work for detailsof this validation and the mesh refinement study (Keoghet al., 2015). A multi-block, completely structured mesh-ing technique was employed and y+ values remained belowone over the wing, endplate and ground plane. The three-dimensional mesh consisted of 7.6x106 cells with 117 in thespanwise direction and and 185 in the chordwise direction.Following a boundary location sensitivity study, the down-stream boundary was located at 50c, and the walls, roof andinlet at 10c from the wing.

(a) isometric view of mesh

(b) mesh across the midspan of the wing

Figure 1. Description of the mesh structure used, consist-ing of 7.6x106 cells in a fully structured domain. The down-stream boundary is located at 50c, and the walls, roof andinlet at 10c from the wing.

For the stationary case, the upstream boundary is a ve-locity inlet set to 30ms−1 and the top and side walls of thedomain are set as stationary walls without shear stress, in or-der to simulate an infinite boundary. The ground surface isset as a moving wall at 30m−1 and the downstream bound-ary is set as a uniform zero pressure.

In the moving case, the upstream boundary is set toa mass flow inlet (with zero flux), the downstream bound-ary as uniform zero pressure and the top and side walls ofthe domain are set as stationary walls. The ground surfaceis set as a moving wall with zero absolute velocity and thesurface of the airfoil is treated as a solid boundary and givena velocity of -30ms−1 . The entire fluid zone for the mov-ing case is also defined as a moving reference frame, beinggiven a translational velocity of -30ms−1.

The Reynolds averaged Navier Stokes (RANS) equa-tion, as follows, is solved.

ρ∂Ui

∂ t+ρU j

∂Ui

∂x j=− ∂P

∂xi+

∂∂x j

(2µS ji−ρu′ju

′i

)(2)

where ρu′ju′i is the Reynolds stress tensor (often written

simply as τi j). Two equation models, such as k-ε models,

2

make use of the Boussinesq eddy viscosity approximationto find the Reynolds stress tensor as a product of the meanstrain rate tensor and an eddy viscosity. We can then repre-sent τi j as:

τi j = µtSi j−23

µt∂uk

∂xkδi j (3)

where µt is the turbulent viscosity and Si j is the modu-lus of the strain rate tensor:

µt = fµ ·Cµρk2

ε(4)

and

Si j =∂ui

∂x j+

∂u j

∂xi(5)

The value calculated for the turbulent viscosity is de-pendent upon factors including the freestream turbulenceintensity, solid boundaries and the flow history effect, whichcan persist for long distances (Wilcox et al., 1998).

Two models for closure of the equations are utilised,the Realizable k-ε model and the linear pressure-strainReynolds Stress Model (RSM) (Launder, 1989). In the stan-dard k-ε model, the model coefficients are constant and de-rived from experiments; in the Realizable k-ε model, Cµ is avariable and the model now ensures positivity of the normalstresses (Shih et al., 1993).

The RSM achieves closure of Equation 2 by the use ofadditional transport equations for the six Reynolds stresses(Launder et al., 1975), and therefore avoids the use of theeddy viscosity assumption on which the k-ε models arebased. It is a physically more complete model, accountingfor flow history, curvature effects, turbulent transport andanisotropy of turbulent stresses.

By implementing the two types of models, with theirassociated levels of complexity, the effect on turbulent gen-eration can be examined.

Table 1. Description of cases studied

Name Reference frame Turbulence model

A stationary realizable k-ε

B stationary RSM

C moving realizable k-ε

D moving RSM

RESULTS AND DISCUSSIONPressure contours on the symmetry plane are presented

in Figure 2, in which the expected general equivalence ofthe reference frames is apparent. The increase in downforce

(a) case A (b) case C

(c) case B (d) case D

Figure 2. Pressure contours on the plane of symmetry, forthe wing at a Reynolds number of 4.54x105 and angle of in-cidence of 3.45o. Cases A and B are in the body-stationaryreference frame and cases C and D are in the body-movingreference frame. Cases A and C utilize the Realizable k-εmodel and cases B and D utilize the RSM.

for a wing in ground effect is seen from the significant in-crease in low pressure existing between the wing suctionsurface and the ground surface.

There are some small differences, however, betweenboth the use of the turbulence model (cases A,C and casesB,D) and the use of the reference frame (cases A,B andcases C,D). These variations are seen particularly on the up-per surface near the trailing edge, and in the suction peakon the lower surface. Taking case A as the baseline, case Bvaries in peak pressure by 7%, case C by 2% and case D by11%.

Considering now the velocity contours on the sym-metry plane in Figure 3, the use of the different referenceframes is clear. Cases A and B are in the typical body-stationary reference frame, where the freestream velocityof 30 ms−1 is visible throughout most of the flowfield. Theslow velocity wake is seen downstream of the wing and be-neath the wing a high velocity region exists, which is notedas the cause of the pressure increase (and therefore increasein downforce).

In our earlier work (Close & Barber, 2014), we foundthat the representation of ground effect flowfields in a body-moving reference frame was beneficial in explaining thefluid dynamics producing the altered aerodynamic charac-teristics. The fluid is seen to be pushed forward at the lead-ing edge, and then under the wing surface, where the highspeed air cause the pressure change between the wing sur-face and the ground. In the wake region, the air is draggedalong with the wing. A small region beneath the wingtrailing edge experiences the flow moving both towards theleading edge, next to the wing surface, and away from theleading edge, in the region between the wing surface andthe ground.

This is demonstrated in Figure 4, where the velocityon a line located along the symmetry plane and at a location2/3 c from the leading edge is plotted. The abrupt changein velocity direction for the body-moving cases is seen, in

3

(a) case A (b) case C

(c) case B (d) case D

Figure 3. Velocity contours on the plane of symmetry, forthe wing at a Reynolds number of 4.54x105 and angle of in-cidence of 3.45o. Cases A and B are in the body-stationaryreference frame and cases C and D are in the body-movingreference frame. Cases A and C utilize the Realizable k-εmodel and cases B and D utilize the RSM.

Figure 4. Velocity on a line located along the symmetryplane and at a location 2/3 c from the leading edge. Cases Aand B are in the body-stationary reference frame and casesC and D are in the body-moving reference frame. Cases Aand C utilize the Realizable k-ε model and cases B and Dutilize the RSM.

contrast to the velocity curves for the body-stationary cases.The effect of the velocity change on the generation of

turbulence is seen in Figure 5. The region closest to thewing surface is shown here to highlight the variation be-tween the four cases. Case A and C show negligible differ-ence however a (very) small variation is observed betweencases B and D. Given that these cases utilize the secondorder RSM closure, the existence of discrepancy due to cur-vature or flow history is more likely to be apparent and theturbulent production generated by the interaction with themean flow is likely to be better represented. However giventhe magnitude of this difference it cannot conclusively beattributed to the reference frame variation.

Considering now the effects in the three-dimensionalplane, the turbulence intensity is found on the ground plane.

Figure 5. Turbulence intensity on a line located along thesymmetry plane and at a location 2/3 c from the leadingedge (showing only the region closest to the wing surface forclarity). Cases A and B are in the body-stationary referenceframe and cases C and D are in the body-moving referenceframe. Cases A and C utilize the Realizable k-ε model andcases B and D utilize the RSM.

(a) case A (b) case C

(c) case B (d) case D

Figure 6. Turbulence intensity contours on the groundplane, noting a symmetry plane reflection as been used forclarity. Cases A and B are in the body-stationary referenceframe and cases C and D are in the body-moving referenceframe. Cases A and C utilize the Realizable k-ε model andcases B and D utilize the RSM.

While shear rates will be negligible for most regions of themoving ground - as the ground is either moving at the samespeed as the air, or both ground and air are stationary - it wasconsidered that the disturbed flow beneath the wing maycontribute to a reference-frame induced flow-field variation.In Figure 6, negligible difference is found between the k-ε model cases, A and C. A small variation is seen for theRSM model cases, B and D, in the region beneath the wing.Again, this difference is very small, but it is significant thatthe variation has been observed only in the more accurateRSM model.

A further examination of the three-dimensional effectsis seen in Figure 7, which displays the velocity magnitude

4

(a) case A, velocity (b) case A, turbulence intensity

(c) case C, velocity (d) case C, turbulence intensity

(e) case B, velocity (f) case B, turbulence intensity

(g) case D, velocity (h) case D, turbulence intensity

Figure 7. Velocity and turbulence intensity contours on aplane 1 c downstream from the leading edge. Cases A and Bare in the body-stationary reference frame and cases C andD are in the body-moving reference frame. Cases A and Cutilize the Realizable k-ε model and cases B and D utilizethe RSM.

and turbulence intensity contours on a plane one chord-length downstream of the wing trailing edge. It is notedthat some variation among all four cases, in these imageswhere the vortex structure can be visualized (as is the vis-cous boundary layer beginning to form on the ground sur-face). The vortex structure forms off the edge of the end-plate, with a primary vortex forming inside the endplate anda secondary vortex formed outside the upper edge of theendplate (Keogh et al., 2015). In the body-moving models,the vortices are seen as regions of high speed air, with a veryclear ground influence (which is not observed as clearly in

(a) Lift coefficients

(b) Drag coefficients

Figure 8. Lift and drag coefficients for the four cases stud-ied. Cases A and B are in the body-stationary referenceframe and cases C and D are in the body-moving referenceframe. Cases A and C utilize the Realizable k-ε model andcases B and D utilize the RSM.

the body-stationary cases). The peak velocity varies be-tween the turbulence models. The k-ε model predicts ahigher level of turbulent flow within the vortex, howeverthe overall shape is similar between the four cases. Bothclosure models show minor variation between the movingand stationary implementations.

There are some small differences to be noted in theforce coefficients calculated for the four cases (Figure 8). Itis not surprising to see some variation between the two clo-sure models, but there is also a variation between the mov-ing and stationary cases, however only for the RSM mod-els. This result follows from the small variations noted inthe flow field for the two cases, and it is expected that somediscrepancy would be then noted in the integrated forces.

CONCLUSIONSA comparison of moving and stationary reference

frames was conducted for two RANS turbulence models,to determine any discrepancies that may arise from the nu-merical implementation of the turbulence present in eachframe. In the stationary case, the wing is assumed to be ina body-stationary reference frame, such as in a wind tunnelsituation. This framework is also used for CFD models ofaerodynamic problems. The real-life case, of course, relatesto a body-moving reference frame, in which the air is quies-cent until disturbed by the wing. In a body-stationary prob-lem, we introduce a non-physical level of turbulence intothe oncoming air. In a moving ground problem, this non-physical disturbance is further compounded by the introduc-tion of a moving surface along the lower boundary whichwill in turn generate additional turbulent (or unsteady) dis-turbances into the freestream.

5

Flow features in both reference frames were presentedto demonstrate the difference in the flow field explanationsthat can occur, and this was highlighted for the region be-neath the wing. Minor differences in results were found,for both velocity and turbulence parameters. Variation wasfound between turbulence models also, as expected.

While some variation in reference frame results maybe attributed to the numerical solution and boundary con-ditions (which were necessarily variant between referenceframes), the larger increase in discrepancy for the RSMdatasets does suggest some reference frame origin for theerror.

However all differences were of a very small value andunlikely to prove any difficulty in using the commonly im-plemented body-stationary situation. A further study mak-ing use of extreme ground effect (less than 5% clearance)is planned, to determine if the error grows in this type ofcondition.

ACKNOWLEDGEMENTSThe authors acknowledge the use of the Trentino High

Performance Computing resource in the School of Mechan-ical and Manufacturing Engineering, University of NewSouth Wales.

REFERENCESAhmed, Mohammed R, Takasaki, T & Kohama, Y 2007

Aerodynamics of a naca4412 airfoil in ground effect.AIAA journal 45 (1), 37–47.

Barber, TJ, Leonardi, E & Archer, RD 1999 A technicalnote on the appropriate cfd boundary conditions for theprediction of ground effect aerodynamics. AeronauticalJournal 103 (1029), 545–547.

Barber, T, Leonardi, E & Archer, RD 2002 Causes for dis-crepancies in ground effect analyses. Aeronautical Jour-nal 106 (1066), 653–668.

Close, P & Barber, T 2014 Explaining ground effect aero-dynamics via a real-life reference frame. In Applied Me-chanics and Materials, , vol. 553, pp. 229–234. TransTech Publ.

Diasinos, S, Barber, TJ, Leonardi, E & Hall, SD 2005 The

Diasinos, S, Barber, TJ, Leonardi, E & Hall, SD 2005 Thevalidation of a 2d cfd model for the implementation ofa moving ground in a unsw wind tunnel. In 5th PacificSymposium on Flow Visualization and Image Processing(PSFVIP5), Daydream Island, Australia.

Doig, G, Barber, T & Diasinos, S 2014 Implications ofcompressibility effects for reynolds–scaled testing of aninverted wing in ground effect. International Journal ofAerodynamics 4 (3), 135–153.

Giacomelli, R 1930 The aerodynamics of leonardo da vinci,jr aeronaut. Soc 34, 1016–1038.

Keogh, J, Doig, G, Diasinos, S & Barber, T 2015 The in-fluence of cornering on the vortical wake structures of aninverted wing. Proc. IMechE. Part D: Journal of Auto-mobile Engineering. in press.

Launder, BE, Reece, G Jr & Rodi, W 1975 Progress inthe development of a reynolds-stress turbulence closure.Journal of fluid mechanics 68 (03), 537–566.

Launder, Brian E 1989 Second-moment closure: presentand future? International Journal of Heat and FluidFlow 10 (4), 282–300.

Lee, S-H & Lee, J 2013 Aerodynamic analysis and multi-objective optimization of wings in ground effect. OceanEngineering 68, 1–13.

Pillai, N, Anil, T, Radhakrishnan, A, Vinod, R, Zaid, Z,Jacob, A & Manojkumar, M 2014 Investigation on airfoiloperating in ground effect region. International Journalof Engineering & Technology 3 (4), 540–544.

Qu, Qiulin, Jia, Xi, Wang, Wei, Liu, Peiqing & Agarwal,Ramesh K 2014 Numerical study of the aerodynamics ofa naca 4412 airfoil in dynamic ground effect. AerospaceScience and Technology 38, 56–63.

Qu, Q, Wang, W, Liu, P & Agarwal, R 2015 Airfoil aero-dynamics in ground effect for wide range of angles ofattack. AIAA Journal pp. 1–14.

Shih, Tsan-Hsing, Zhu, Jiang & Lumley, John L 1993A realizable reynolds stress algebraic equation model.Linthicum Heights, MD: NASA Center for AeroSpace In-formation,— c1993 1.

Wilcox, David C et al. 1998 Turbulence modeling for CFD,, vol. 2. DCW industries La Canada, CA.

Zerihan, J & Zhang, X 2000 Aerodynamics of a single el-ement wing in ground effect. Journal of Aircraft 37 (6),1058–1064.

6